📚 Year 7 CCEA Engineering: Formula & Theorem Quick Reference | CCEA 七年级工程：公式定理速查手册
This quick reference handbook brings together all the essential formulas, theorems and principles that Year 7 CCEA Engineering students need to know. From forces and motion to electrical circuits and mechanical advantage, each section presents a concept in clear English followed immediately by its Chinese translation, making it ideal for bilingual revision.
本速查手册汇集了CCEA七年级工程学科所有必备的公式、定理与基本原理。从力与运动到电路与机械利益，每个小节都用清晰的英文讲解紧接着对应的中文翻译，非常适合双语复习。
1. Force and Newton’s Laws | 力与牛顿定律
Force is a push or a pull that can change an object’s motion. It is measured in newtons (N). An unbalanced force causes acceleration, while balanced forces result in no change in motion.
力是能够改变物体运动状态的推或拉，单位是牛顿（N）。不平衡的力会产生加速度，而平衡力则不会改变运动状态。
F = m × a
Newton’s Second Law is summarized by F = m × a. Here, F is force in newtons, m is mass in kilograms (kg), and a is acceleration in metres per second squared (m/s²). A larger force produces a larger acceleration for a given mass.
牛顿第二定律可概括为 F = m × a。其中 F 是力（牛顿），m 是质量（千克，kg），a 是加速度（米/秒²，m/s²）。对于给定的质量，力越大产生的加速度也越大。
Newton’s Third Law states that for every action force there is an equal and opposite reaction force. When you push against a wall, the wall pushes back with the same strength in the opposite direction.
牛顿第三定律指出，每一个作用力都有一个大小相等、方向相反的反作用力。当你推墙时，墙会以同样大小的力反方向推你。
2. Pressure in Solids and Fluids | 固体与流体中的压力
Pressure describes how concentrated a force is over an area. It is calculated as force per unit area.
压力描述了力在面积上的集中程度，计算公式为力除以面积。
P = F / A
P is pressure in pascals (Pa) or N/m², F is force in newtons, and A is the area in square metres (m²). A sharp knife cuts easily because the same force is applied over a much smaller area, creating high pressure.
P 为压力（帕斯卡 Pa 或 N/m²），F 为力（牛顿），A 为面积（平方米 m²）。锋利的刀容易切割，因为同样的力作用在更小的面积上，产生了更高的压力。
In liquids and gases, pressure acts equally in all directions at a given depth. The deeper you go in a liquid, the greater the pressure because of the weight of the fluid above.
在液体和气体中，同一深度处的压力在各个方向上大小相等。液体中越深的地方压力越大，这是因为上方液体的重量增加了。
3. Moments and Levers | 力矩与杠杆
A moment is the turning effect of a force about a pivot. It tells us how easily something can be rotated.
力矩是力对支点产生的转动效果，它反映了使物体转动的容易程度。
M = F × d
M is the moment in newton‑metres (Nm), F is the force in newtons, and d is the perpendicular distance from the pivot to the line of action of the force in metres (m). To increase the moment, you can apply a larger force or increase the distance from the pivot.
M 是力矩（牛顿·米 Nm），F 是力（牛顿），d 是力到支点的垂直距离（米 m）。要增大力矩，可以加大作用力或增加力与支点间的距离。
For a lever to balance, the clockwise moment must equal the anticlockwise moment. This principle of moments is used in tools like crowbars and seesaws.
要让杠杆平衡，顺时针力矩必须等于逆时针力矩。这一力矩原理被应用在撬棍和跷跷板等工具中。
4. Work, Energy and Power | 功、能与功率
Work is done when a force moves an object through a distance. Energy is the ability to do work, and both are measured in joules (J).
当一个力使物体移动一段距离时就做了功。能量是做功的本领，功和能量的单位都是焦耳（J）。
W = F × d
Work W equals the applied force F (in newtons) multiplied by the distance d (in metres) moved in the direction of the force. If you lift a 10 N weight by 2 m, you do 20 J of work.
功 W 等于作用力 F（牛顿）乘以物体在力的方向上移动的距离 d（米）。将 10 N 的重物提升 2 m，做功为 20 J。
P = W / t
Power P is the rate of doing work, measured in watts (W). One watt equals one joule per second. A machine with higher power can do the same amount of work in less time.
功率 P 是做功的快慢，单位是瓦特（W）。1 瓦特等于每秒 1 焦耳。功率越大的机器，完成同样的功所需时间越短。
5. Efficiency | 效率
Efficiency measures how well a device converts input energy into useful output energy. No machine is perfectly efficient because some energy is always lost to heat, sound or friction.
效率衡量的是设备将输入能量转换为有用输出能量的程度。由于总有能量会以热、声音或摩擦的形式损耗，没有机器能达到百分之百的效率。
Efficiency = (Useful Output Energy / Total Input Energy) × 100%
Efficiency is often expressed as a percentage. The useful output energy is always less than the total input. For example, an electric motor that wastes 30 J of heat for every 100 J of electrical energy supplied has an efficiency of 70%.
效率常用百分数表示。有用输出能量总是小于总输入能量。例如，一个电动机每消耗 100 J 电能就有 30 J 以热的形式浪费，效率为 70%。
Efficiency can also be expressed in terms of power: Efficiency = (Useful Power Output / Total Power Input) × 100%. Reducing friction and using lubrication are practical ways to improve efficiency.
效率也可以用功率表示：效率 = (有用输出功率 / 总输入功率) × 100%。减少摩擦和使用润滑剂是提高效率的常用方法。
6. Mechanical Advantage (MA) | 机械利益
Mechanical advantage tells you how much a machine multiplies the effort force. It is a ratio of the load lifted to the effort applied.
机械利益表示机器将作用力放大了多少倍，它是被升起的负载与施加的动力之比。
MA = Load / Effort
In a simple lever, if a 200 N load can be lifted using an effort of only 50 N, the mechanical advantage is 4. An MA greater than 1 means the machine reduces the effort needed.
在简单杠杆中，如果 200 N 的负载只需 50 N 的动力就能抬起，那么机械利益为 4。MA 大于 1 意味着机器减小了所需的作用力。
For levers, MA can also be expressed as the ratio of the effort arm length to the load arm length. In pulleys and gears, the number of ropes or teeth determines the mechanical advantage.
对于杠杆，机械利益也可表示为动力臂长度与负载臂长度之比。在滑轮和齿轮系统中，绳索段数或齿数决定了机械利益的大小。
7. Speed, Velocity and Acceleration | 速率、速度与加速度
Speed is a scalar quantity measuring how fast an object moves, while velocity is a vector quantity that includes direction. Both are often expressed in metres per second (m/s).
速率是标量，描述物体运动快慢；速度是矢量，包含方向。两者的常用单位都是米/秒（m/s）。
v = d / t
Average speed v is distance d divided by time t. If a bicycle travels 100 m in 20 s, its average speed is 5 m/s. Velocity uses displacement instead of total distance.
平均速率 v 等于距离 d 除以时间 t。若一辆自行车 20 秒内行驶 100 m，平均速率为 5 m/s。速度则用位移代替总路程。
a = (v – u) / t
Acceleration a is the change in velocity per unit time, where u is initial velocity, v is final velocity and t is time. A negative acceleration means deceleration (slowing down).
加速度 a 是单位时间内速度的变化量，u 为初速度，v 为末速度，t 为时间。负的加速度表示减速。
8. Ohm’s Law and Basic Circuits | 欧姆定律与基础电路
Ohm’s Law links potential difference (voltage), current and resistance in a circuit. It is the foundation for understanding how electrical components behave.
欧姆定律将电路中的电压、电流和电阻联系起来，是理解电子元件工作原理的基础。
V = I × R
V is the voltage in volts (V), I is the current in amperes (A), and R is the resistance in ohms (Ω). If a resistor of 10 Ω has a current of 2 A flowing through it, the voltage across it is 20 V.
V 为电压（伏特 V），I 为电流（安培 A），R 为电阻（欧姆 Ω）。若一个 10 Ω 的电阻中流过 2 A 的电流，其两端电压为 20 V。
In a series circuit, the current is the same everywhere, but the voltage splits across components. In a parallel circuit, the voltage is the same across each branch, while the current splits at junctions.
在串联电路中，电流处处相等，但电压在各元件间分配。在并联电路中，各支路两端电压相同，而电流在节点处分流。
9. Resistors in Series and Parallel | 电阻的串联与并联
When resistors are connected in series, the total resistance is simply the sum of all individual resistances because the current must pass through each resistor one after another.
当电阻串联时，总电阻等于各个电阻之和，因为电流必须依次通过每个电阻。
Rtotal = R₁ + R₂ + R₃ + …
For example, a 5 Ω and a 10 Ω resistor in series give a total resistance of 15 Ω. This increases the overall resistance and reduces the current for a given voltage.
例如，一只 5 Ω 和一只 10 Ω 的电阻串联，总电阻为 15 Ω。这会增大总电阻，在给定电压下减小电流。
For resistors in parallel, the total resistance is less than the smallest individual resistance because the current has multiple paths.
电阻并联时，总电阻小于其中最小的单个电阻，因为电流有多个通路。
1 / Rtotal = 1 / R₁ + 1 / R₂ + …
For two resistors in parallel, a shortcut formula is often used: Rtotal = (R₁ × R₂) / (R₁ + R₂). Two 10 Ω resistors in parallel give a total resistance of 5 Ω.
对于两个并联电阻，常使用简化公式：Rtotal = (R₁ × R₂) / (R₁ + R₂)。两只 10 Ω 电阻并联，总电阻为 5 Ω。
10. Gear Ratios and Transmission | 齿轮比与传动
Gears transmit rotational motion and can change speed, torque and direction. The gear ratio compares the number of teeth on two meshing gears.
齿轮用于传递转动，并能改变转速、扭矩和方向。齿轮比是相啮合的两个齿轮齿数的比值。
Gear Ratio = Number of teeth on driven gear / Number of teeth on driver gear
If a 40‑tooth gear drives a 20‑tooth gear, the gear ratio is 20/40 = 0.5 (or 1:2). This means the driven gear turns twice as fast but with half the torque.
如果一个 40 齿齿轮驱动一个 20 齿齿轮，齿轮比为 20/40 = 0.5（或 1:2）。这意味着从动轮转速加倍，但扭矩减半。
When a smaller gear drives a larger gear, the output speed decreases but the torque increases — this is called a speed reduction system. The opposite gives a speed‑increasing system.
小齿轮驱动大齿轮时，输出转速降低但扭矩增大，称为减速系统；反之则为增速系统。
Compound gears combine several pairs to achieve larger overall ratios. The total ratio is the product of the individual ratios.
复合齿轮将多对齿轮组合以获得更大的总传动比。总传动比等于各级传动比之积。
11. Density | 密度
Density is a measure of how much mass is packed into a given volume. It helps engineers choose materials for strength, buoyancy and weight requirements.
密度是单位体积内所含质量的量度，有助于工程师根据强度、浮力和重量要求选择材料。
ρ = m / V
The symbol ρ (rho) stands for density, m is mass in kilograms (kg), and V is volume in cubic metres (m³). The SI unit of density is kg/m³, but g/cm³ is also common.
符号 ρ (rho) 表示密度，m 为质量（千克 kg），V 为体积（立方米 m³）。密度的国际单位是 kg/m³，也常用 g/cm³。
Pure water has a density of 1000 kg/m³ (or 1 g/cm³). Materials with a density less than water will float, while those with higher density will sink.
纯水的密度为 1000 kg/m³（即 1 g/cm³）。密度小于水的物体会浮起，密度大于水的则会沉下。
12. Stress and Strain – Basic Engineering Concepts | 应力与应变——基本工程概念
Stress measures the internal force per unit area within a material when an external load is applied. Strain measures how much the material deforms relative to its original length.
应力是材料在外力作用下单位面积上的内力。应变则是材料相对于原始长度的变形程度。
Stress = F / A
Stress has the same units as pressure (Pa or N/m²). Tensile stress stretches a material, compressive stress squeezes it, and shear stress causes sliding.
应力的单位与压力相同（Pa 或 N/m²）。拉伸应力使材料伸长，压缩应力使其缩短，剪切应力导致层间滑移。
Strain = ΔL / L₀
Strain is a dimensionless number: elongation ΔL divided by the original length L₀. A steel rod that stretches by 0.1 mm over an original 100 mm length experiences a strain of 0.001.
应变是无量纲数：伸长量 ΔL 除以原始长度 L₀。一根 100 mm 长的钢棒伸长 0.1 mm，应变为 0.001。
Although Year 7 students only meet stress and strain at an introductory level, understanding these concepts helps when designing structures that must not break under load.
虽然七年级学生只初步接触应力与应变，但理解这些概念有助于设计在载荷下不会破坏的结构。
Published by TutorHao | Engineering Revision Series | aleveler.com
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